The Scattering Map on Oppenheimer-Snyder Space-Time
The Scattering Map on Oppenheimer-Snyder Space-Time
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奥本海默-斯奈德时空散射图
DOI：
10.1007/s00023-020-00905-5
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Alford F
中科院分区：
文献类型：
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作者：
Alford F
本文分析了Oppenheimer-Snyder引力坍缩模型中反射尘埃云和渗透尘埃云两种情况下波动方程解的有界性。然后我们继续定义这个时空上的散射图，并看看我们在这个散射图上的有界性结果的含义。具体地说，在反射和渗透情况下，能量在时间上向前和向后都保持均匀有界。然后证明了散射图是向前有界的，而不是向后有界的。因此，散射映射在有限能量空间上不是满射的。因此，不存在从有限能量辐射场到有限能量辐射场的反向散射映射。然后我们将它与纯史瓦西散射的情况进行对比。
In this paper, we analyse the boundedness of solutionsof the wave equation in the Oppenheimer–Snyder model of gravitational collapse in both the case of a reflective dust cloud and a permeating dust cloud. We then proceed to define the scattering map on this space-time and look at the implications of our boundedness results on this scattering map. Specifically, it is shown that the energy ofremains uniformly bounded going forwards in time and going backwards in time for both the reflective and the permeating cases. It is then shown that the scattering map is bounded going forwards, but not backwards. Therefore, the scattering map is not surjective onto the space of finite energy on. Thus, there does not exist a backwards scattering map from finite energy radiation fields onto finite energy radiation fields on. We will then contrast this with the situation for scattering in pure Schwarzschild.